Related papers: Decay of one dimensional surface modulations
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited…
The temporal evolution of equilibrium fluctuations for surface steps of monoatomic height is analyzed studying one-dimensional solid-on-solid models. Using Monte Carlo simulations, fluctuations due to periphery-diffusion (PD) as well as due…
We consider methods of interpolating between the crystalline and dynamically triangulated random surface models. We argue that actions based on the deviation from six of the coordination number at a site are inadequate and propose an…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature…
We investigate the scaling properties of the interface fluctuation width for the $Q$-mer and $Q$-particle-correlated deposition-evaporation models. These models are constrained with a global conservation law that the particle number at each…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
The finite-size scaling function and the leading corrections for the single species 1D coagulation model $(A + A \rightarrow A)$ and the annihilation model $(A + A \rightarrow \emptyset)$ are calculated. The scaling functions are universal…
Fluctuations of isolated and pairs of ascending steps of monoatomic height are studied in the framework of SOS models, using mainly Monte Carlo techniques. Below the roughening transistion of the surface, the profiles of long steps show the…
We show that smoothing of multiaffine surfaces that are generated by simulating a crosslinked polymer gel by a frustrated, triangular network of springs of random equilibrium lengths [G.M. Buend{\'\i}a, S.J. Mitchell, P.A. Rikvold, Phys.…
The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both…
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…
We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t =…
Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations…